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An upper bound on the number of simple directed rooted graphs on 𝑛 vertices?

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Harary in "The number of linear, directed, rooted, and connected graphs" 
treats, IMHO, the cases of rooted undirected graphs and unrooted 
directed graphs. I believe that someone must have computed the number of 
rooted directed graphs up to isomorphism, but I failed to find a 
reference so far. Could anyone help? I consider only simple graphs, 
which have no multiple edges or graph loops (corresponding to a binary 
adjacency matrix with 0s on the diagonal). Two graphs are considered the 
same iff there is a bijection between the vertices that induces a 
bijection on the edges and sends the root of one graph to the root of 
the other.

That is, the number of pairwise nonisomorphic simple rooted directed 
graphs on n vertices is asked for. A good upper bound would suffice.

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An upper bound on the number of simple directed rooted graphs on 𝑛 vertices? Just a man <Just_A_ManFUCKSPAM@mein.SPAMFUCKgmx> - 2020-01-14 21:10 +0100

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